The court said in a statement that the request from the National Force Union had been denied due to previous public order violations.
Authorities in Riga had earlier turned down three other applications by a number of groups to stage the event. The only organization that will be allowed to hold a short street march on Sunday is the WWII veterans group, Daugavas Vanagi.
A Latvian Legion march in 2005 through Riga resulted in dozens of arrests after clashes with Russian activists. The march involved WWII SS veterans and young nationalists.
The march commemorated a historic battle in March 1944 between the Soviet and German armies on the banks of the Velikaya River, northwestern Russia.
Soviet troops began their assault on March 16, forcing German Waffen-SS divisions to withdraw. However Latvian troops held their lines and prevented the Soviets from advancing further.
Relations between Russia, Latvia and Estonia have been marred in the past few years by what Moscow calls the unequal treatment of ethnic Russians, the alleged persecution of Soviet WWII veterans, and the apparent revival of nationalism and fascism in the Baltic States.
Latvia has been criticized by Amnesty International for its treatment of its 400,000 Russian-speaking population, many of whom continue to live in the country without Latvian citizenship.